different LED's require different voltages, Red being the brightest with the least (something to do with the band gap, wavelengths and things I never understood)

White for example will light dimly from a 3v cell coin, but a Red will shine really brightly... so if you used a white led, combine it with a voltage drop 3.3v, you're at the limit's a 5v would be better that's all.

Are you certain that is a TIP120 (NPN), and not a TIP125 (PNP)? Under these conditions, the TIP125 would keep the LED lit no matter the voltage on the base. Look at the polarity of the collector-emitter diode in the product schematic. Left is NPN, right is PNP.

For that TIP120, the VCE @ IC=20ma would be about 0.5V. So your measurement of that value is fine, but it indicates the darlington is on, as does the fact that the LED is on.

The diagram looks right but I'd change some of the values. Since the gain is so high (more than 1000 for a TIP120), that 1K resistor on the base could/should be more like 100K for turning on an LED. Also, the LED resistor should be about 75ohms given the that supply voltage is 3.3V. Try those values.

Also, have you verified that the signal from D3 is actually going high and low? If it is, then check over your wiring again.

Another thing you could try, since the TIP120 is huge overkill for this situation, is a simple little NPN transistor like a 2N3904 or 2N2222. if you try the little transistor, use 4K7 for the base resistor and still use 75ohms for the LED resistor.

Take a look on top, i had a problem with my supplier. I ordered some TIP 120 and i had some TIP 135 (PNP). The "funny" thing is that the box was labeled TIP120 but inside, there was some TIP135, and i didn't check it... Was my fault

I know that the TIP120 is much more than necessary in this case, but the led was here only for a test purpose. In the end i'll put 2 led lights for an amount of 40W